The London 2012 Olympic and Paralympic Games have come in £377m under budget, according to the latest government figures.

The overall cost of the Games is forecast to be £8.921bn from a budget of £9.298bn.

With some contracts still to be wound up after the end of the Games, ministers are describing the underspend as a "prudent" estimate. The sports minister, Hugh Robertson, described the feat of managing the complex programme within budget as "a tremendous success".

He said: "The work of the construction and delivery teams, from the ODA [Olympic Delivery Authority] and Locog [London Organising Committee of the Olympic and Paralympic Games], has set a very high standard and I have no doubt that London 2012 has set a new benchmark for the management of Olympic and Paralympic Games in future."

Talks are also still ongoing between the London 2012 organisers and G4S to get the security firm to pay back money for the fiasco over its failure to provide enough security guards for the Games.

Robertson said: "There are projected savings of at least £377m so the prediction that I made this summer that we could bring this project in at under £9bn has almost certainly been met.

"The £377m figure is conservative because there are lumps of contingency that are still attached to the outstanding work. The central expectation has to be in line with the rest of the project that not all of that will be needed.

"Locog also have to conclude, and we have to sign off, the negotiations with G4S over the size of the amount of money that will be paid back to the public purse – so if you were to add to that £377m, anything that will not be used but is held against outstanding work and anything that might come back from G4S, it is entirely reasonable to expect that figure to rise."

Some £103m of contingency is being held to cover the remaining risks in the programme. These include the retrofit of the Olympic Village to get it ready for use when it reopens after the Games.

There are also around 2,000 contracts with the ODA, the Olympic builders and London 2012 that still have to be closed out. In addition, £480m of uncommitted contingency still remains within the budget.

The ODA's construction and transport programme has come in at £6.714bn, according to the estimates. This is a drop of £47m on the previous estimated figure. The savings made by the ODA are now at £1.032bn.

Overall savings have been made through "really tough project management" by London 2012, ODA and the government, according to Robertson.